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Constraining the emergent dark energy models with observational data at intermediate redshift (2404.14237v3)

Published 22 Apr 2024 in astro-ph.CO

Abstract: In this work, we investigate the phenomenologically emergent dark energy (PEDE) model and its generalized form, namely the generalized emergent dark energy (GEDE) model, which introduces a free parameter \unboldmath {( \Delta )} that can discriminate between the \unboldmath{$\mathrm{\Lambda}$}CDM model and the PEDE model. Fitting the emergent dark energy (EDE) models with the observational datasets including the cosmology-independent gamma-ray bursts (GRBs) and the observational Hubble data (OHD) at intermediate redshift, we find a large value of $H_0$ which is close to the results of local measurement of $H_0$ from the SH0ES Collaboration in both EDE models. In order to refine our analysis and tighten the constraints on cosmological parameters, we combine mid-redshift observations GRBs and OHD with baryon acoustic oscillations (BAOs). Finally, we constrain DE models by using the simultaneous fitting method, in which the parameters of DE models and the relation parameters of GRBs are fitted simultaneously. Our results suggest that PEDE and GEDE models can serve as an important supplement and be possible alternative to the standard cosmological model, pending further theoretical explorations and observational verifications.

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References (62)
  1. Perlmutter, S., Aldering, G., Goldhaber, G., et al.: Measurements of ΩΩ\Omegaroman_Ω and ΛΛ\Lambdaroman_Λ from 42 High-Redshift Supernovae. The Astrophysical Journal 517(2), 565 (1999) https://doi.org/10.1086/307221 Riess et al. [2007] Riess, A.G., Strolger, L.-G., Casertano, S., et al.: New Hubble Space Telescope Discoveries of Type Ia Supernovae at z ≥\geq≥ 1: Narrowing Constraints on the Early Behavior of Dark Energy. The Astrophysical Journal 659(1), 98 (2007) https://doi.org/10.1086/510378 Scolnic et al. [2018] Scolnic, D.M., Jones, D.O., Rest, A., et al.: The Complete Light-curve Sample of Spectroscopically Confirmed SNe Ia from Pan-STARRS1 and Cosmological Constraints from the Combined Pantheon Sample. The Astrophysical Journal 859(2), 101 (2018) https://doi.org/10.3847/1538-4357/aab9bb Beutler et al. [2011] Beutler, F., Blake, C., Colless, M., et al.: The 6dF Galaxy Survey: baryon acoustic oscillations and the local Hubble constant. Monthly Notices of the Royal Astronomical Society 416(4), 3017 (2011) https://doi.org/10.1111/j.1365-2966.2011.19250.x Ross et al. [2015] Ross, A.J., Samushia, L., Howlett, C., et al.: The clustering of the SDSS DR7 main Galaxy sample - I. A 4 per cent distance measure at z = 0.15. Monthly Notices of the Royal Astronomical Society 449(1), 835 (2015) https://doi.org/10.1093/mnras/stv154 Alam et al. [2017] Alam, U., Bag, S., Sahni, V.: Constraining the cosmology of the phantom brane using distance measures. Physical Review D 95(2), 023524 (2017) https://doi.org/10.1103/PhysRevD.95.023524 Zhao et al. [2019] Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Strolger, L.-G., Casertano, S., et al.: New Hubble Space Telescope Discoveries of Type Ia Supernovae at z ≥\geq≥ 1: Narrowing Constraints on the Early Behavior of Dark Energy. The Astrophysical Journal 659(1), 98 (2007) https://doi.org/10.1086/510378 Scolnic et al. [2018] Scolnic, D.M., Jones, D.O., Rest, A., et al.: The Complete Light-curve Sample of Spectroscopically Confirmed SNe Ia from Pan-STARRS1 and Cosmological Constraints from the Combined Pantheon Sample. The Astrophysical Journal 859(2), 101 (2018) https://doi.org/10.3847/1538-4357/aab9bb Beutler et al. [2011] Beutler, F., Blake, C., Colless, M., et al.: The 6dF Galaxy Survey: baryon acoustic oscillations and the local Hubble constant. Monthly Notices of the Royal Astronomical Society 416(4), 3017 (2011) https://doi.org/10.1111/j.1365-2966.2011.19250.x Ross et al. [2015] Ross, A.J., Samushia, L., Howlett, C., et al.: The clustering of the SDSS DR7 main Galaxy sample - I. A 4 per cent distance measure at z = 0.15. Monthly Notices of the Royal Astronomical Society 449(1), 835 (2015) https://doi.org/10.1093/mnras/stv154 Alam et al. [2017] Alam, U., Bag, S., Sahni, V.: Constraining the cosmology of the phantom brane using distance measures. Physical Review D 95(2), 023524 (2017) https://doi.org/10.1103/PhysRevD.95.023524 Zhao et al. [2019] Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Scolnic, D.M., Jones, D.O., Rest, A., et al.: The Complete Light-curve Sample of Spectroscopically Confirmed SNe Ia from Pan-STARRS1 and Cosmological Constraints from the Combined Pantheon Sample. The Astrophysical Journal 859(2), 101 (2018) https://doi.org/10.3847/1538-4357/aab9bb Beutler et al. [2011] Beutler, F., Blake, C., Colless, M., et al.: The 6dF Galaxy Survey: baryon acoustic oscillations and the local Hubble constant. Monthly Notices of the Royal Astronomical Society 416(4), 3017 (2011) https://doi.org/10.1111/j.1365-2966.2011.19250.x Ross et al. [2015] Ross, A.J., Samushia, L., Howlett, C., et al.: The clustering of the SDSS DR7 main Galaxy sample - I. A 4 per cent distance measure at z = 0.15. Monthly Notices of the Royal Astronomical Society 449(1), 835 (2015) https://doi.org/10.1093/mnras/stv154 Alam et al. [2017] Alam, U., Bag, S., Sahni, V.: Constraining the cosmology of the phantom brane using distance measures. Physical Review D 95(2), 023524 (2017) https://doi.org/10.1103/PhysRevD.95.023524 Zhao et al. [2019] Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Beutler, F., Blake, C., Colless, M., et al.: The 6dF Galaxy Survey: baryon acoustic oscillations and the local Hubble constant. Monthly Notices of the Royal Astronomical Society 416(4), 3017 (2011) https://doi.org/10.1111/j.1365-2966.2011.19250.x Ross et al. [2015] Ross, A.J., Samushia, L., Howlett, C., et al.: The clustering of the SDSS DR7 main Galaxy sample - I. A 4 per cent distance measure at z = 0.15. Monthly Notices of the Royal Astronomical Society 449(1), 835 (2015) https://doi.org/10.1093/mnras/stv154 Alam et al. [2017] Alam, U., Bag, S., Sahni, V.: Constraining the cosmology of the phantom brane using distance measures. Physical Review D 95(2), 023524 (2017) https://doi.org/10.1103/PhysRevD.95.023524 Zhao et al. [2019] Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ross, A.J., Samushia, L., Howlett, C., et al.: The clustering of the SDSS DR7 main Galaxy sample - I. A 4 per cent distance measure at z = 0.15. Monthly Notices of the Royal Astronomical Society 449(1), 835 (2015) https://doi.org/10.1093/mnras/stv154 Alam et al. [2017] Alam, U., Bag, S., Sahni, V.: Constraining the cosmology of the phantom brane using distance measures. Physical Review D 95(2), 023524 (2017) https://doi.org/10.1103/PhysRevD.95.023524 Zhao et al. [2019] Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Alam, U., Bag, S., Sahni, V.: Constraining the cosmology of the phantom brane using distance measures. Physical Review D 95(2), 023524 (2017) https://doi.org/10.1103/PhysRevD.95.023524 Zhao et al. [2019] Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  2. Riess, A.G., Strolger, L.-G., Casertano, S., et al.: New Hubble Space Telescope Discoveries of Type Ia Supernovae at z ≥\geq≥ 1: Narrowing Constraints on the Early Behavior of Dark Energy. The Astrophysical Journal 659(1), 98 (2007) https://doi.org/10.1086/510378 Scolnic et al. [2018] Scolnic, D.M., Jones, D.O., Rest, A., et al.: The Complete Light-curve Sample of Spectroscopically Confirmed SNe Ia from Pan-STARRS1 and Cosmological Constraints from the Combined Pantheon Sample. The Astrophysical Journal 859(2), 101 (2018) https://doi.org/10.3847/1538-4357/aab9bb Beutler et al. [2011] Beutler, F., Blake, C., Colless, M., et al.: The 6dF Galaxy Survey: baryon acoustic oscillations and the local Hubble constant. Monthly Notices of the Royal Astronomical Society 416(4), 3017 (2011) https://doi.org/10.1111/j.1365-2966.2011.19250.x Ross et al. [2015] Ross, A.J., Samushia, L., Howlett, C., et al.: The clustering of the SDSS DR7 main Galaxy sample - I. A 4 per cent distance measure at z = 0.15. Monthly Notices of the Royal Astronomical Society 449(1), 835 (2015) https://doi.org/10.1093/mnras/stv154 Alam et al. [2017] Alam, U., Bag, S., Sahni, V.: Constraining the cosmology of the phantom brane using distance measures. Physical Review D 95(2), 023524 (2017) https://doi.org/10.1103/PhysRevD.95.023524 Zhao et al. [2019] Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Scolnic, D.M., Jones, D.O., Rest, A., et al.: The Complete Light-curve Sample of Spectroscopically Confirmed SNe Ia from Pan-STARRS1 and Cosmological Constraints from the Combined Pantheon Sample. The Astrophysical Journal 859(2), 101 (2018) https://doi.org/10.3847/1538-4357/aab9bb Beutler et al. [2011] Beutler, F., Blake, C., Colless, M., et al.: The 6dF Galaxy Survey: baryon acoustic oscillations and the local Hubble constant. Monthly Notices of the Royal Astronomical Society 416(4), 3017 (2011) https://doi.org/10.1111/j.1365-2966.2011.19250.x Ross et al. [2015] Ross, A.J., Samushia, L., Howlett, C., et al.: The clustering of the SDSS DR7 main Galaxy sample - I. A 4 per cent distance measure at z = 0.15. Monthly Notices of the Royal Astronomical Society 449(1), 835 (2015) https://doi.org/10.1093/mnras/stv154 Alam et al. [2017] Alam, U., Bag, S., Sahni, V.: Constraining the cosmology of the phantom brane using distance measures. Physical Review D 95(2), 023524 (2017) https://doi.org/10.1103/PhysRevD.95.023524 Zhao et al. [2019] Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Beutler, F., Blake, C., Colless, M., et al.: The 6dF Galaxy Survey: baryon acoustic oscillations and the local Hubble constant. Monthly Notices of the Royal Astronomical Society 416(4), 3017 (2011) https://doi.org/10.1111/j.1365-2966.2011.19250.x Ross et al. [2015] Ross, A.J., Samushia, L., Howlett, C., et al.: The clustering of the SDSS DR7 main Galaxy sample - I. A 4 per cent distance measure at z = 0.15. Monthly Notices of the Royal Astronomical Society 449(1), 835 (2015) https://doi.org/10.1093/mnras/stv154 Alam et al. [2017] Alam, U., Bag, S., Sahni, V.: Constraining the cosmology of the phantom brane using distance measures. Physical Review D 95(2), 023524 (2017) https://doi.org/10.1103/PhysRevD.95.023524 Zhao et al. [2019] Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ross, A.J., Samushia, L., Howlett, C., et al.: The clustering of the SDSS DR7 main Galaxy sample - I. A 4 per cent distance measure at z = 0.15. Monthly Notices of the Royal Astronomical Society 449(1), 835 (2015) https://doi.org/10.1093/mnras/stv154 Alam et al. [2017] Alam, U., Bag, S., Sahni, V.: Constraining the cosmology of the phantom brane using distance measures. Physical Review D 95(2), 023524 (2017) https://doi.org/10.1103/PhysRevD.95.023524 Zhao et al. [2019] Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Alam, U., Bag, S., Sahni, V.: Constraining the cosmology of the phantom brane using distance measures. Physical Review D 95(2), 023524 (2017) https://doi.org/10.1103/PhysRevD.95.023524 Zhao et al. [2019] Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  3. Scolnic, D.M., Jones, D.O., Rest, A., et al.: The Complete Light-curve Sample of Spectroscopically Confirmed SNe Ia from Pan-STARRS1 and Cosmological Constraints from the Combined Pantheon Sample. The Astrophysical Journal 859(2), 101 (2018) https://doi.org/10.3847/1538-4357/aab9bb Beutler et al. [2011] Beutler, F., Blake, C., Colless, M., et al.: The 6dF Galaxy Survey: baryon acoustic oscillations and the local Hubble constant. Monthly Notices of the Royal Astronomical Society 416(4), 3017 (2011) https://doi.org/10.1111/j.1365-2966.2011.19250.x Ross et al. [2015] Ross, A.J., Samushia, L., Howlett, C., et al.: The clustering of the SDSS DR7 main Galaxy sample - I. A 4 per cent distance measure at z = 0.15. Monthly Notices of the Royal Astronomical Society 449(1), 835 (2015) https://doi.org/10.1093/mnras/stv154 Alam et al. [2017] Alam, U., Bag, S., Sahni, V.: Constraining the cosmology of the phantom brane using distance measures. Physical Review D 95(2), 023524 (2017) https://doi.org/10.1103/PhysRevD.95.023524 Zhao et al. [2019] Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Beutler, F., Blake, C., Colless, M., et al.: The 6dF Galaxy Survey: baryon acoustic oscillations and the local Hubble constant. Monthly Notices of the Royal Astronomical Society 416(4), 3017 (2011) https://doi.org/10.1111/j.1365-2966.2011.19250.x Ross et al. [2015] Ross, A.J., Samushia, L., Howlett, C., et al.: The clustering of the SDSS DR7 main Galaxy sample - I. A 4 per cent distance measure at z = 0.15. Monthly Notices of the Royal Astronomical Society 449(1), 835 (2015) https://doi.org/10.1093/mnras/stv154 Alam et al. [2017] Alam, U., Bag, S., Sahni, V.: Constraining the cosmology of the phantom brane using distance measures. Physical Review D 95(2), 023524 (2017) https://doi.org/10.1103/PhysRevD.95.023524 Zhao et al. [2019] Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ross, A.J., Samushia, L., Howlett, C., et al.: The clustering of the SDSS DR7 main Galaxy sample - I. A 4 per cent distance measure at z = 0.15. Monthly Notices of the Royal Astronomical Society 449(1), 835 (2015) https://doi.org/10.1093/mnras/stv154 Alam et al. [2017] Alam, U., Bag, S., Sahni, V.: Constraining the cosmology of the phantom brane using distance measures. Physical Review D 95(2), 023524 (2017) https://doi.org/10.1103/PhysRevD.95.023524 Zhao et al. [2019] Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Alam, U., Bag, S., Sahni, V.: Constraining the cosmology of the phantom brane using distance measures. Physical Review D 95(2), 023524 (2017) https://doi.org/10.1103/PhysRevD.95.023524 Zhao et al. [2019] Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  4. Beutler, F., Blake, C., Colless, M., et al.: The 6dF Galaxy Survey: baryon acoustic oscillations and the local Hubble constant. Monthly Notices of the Royal Astronomical Society 416(4), 3017 (2011) https://doi.org/10.1111/j.1365-2966.2011.19250.x Ross et al. [2015] Ross, A.J., Samushia, L., Howlett, C., et al.: The clustering of the SDSS DR7 main Galaxy sample - I. A 4 per cent distance measure at z = 0.15. Monthly Notices of the Royal Astronomical Society 449(1), 835 (2015) https://doi.org/10.1093/mnras/stv154 Alam et al. [2017] Alam, U., Bag, S., Sahni, V.: Constraining the cosmology of the phantom brane using distance measures. Physical Review D 95(2), 023524 (2017) https://doi.org/10.1103/PhysRevD.95.023524 Zhao et al. [2019] Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ross, A.J., Samushia, L., Howlett, C., et al.: The clustering of the SDSS DR7 main Galaxy sample - I. A 4 per cent distance measure at z = 0.15. Monthly Notices of the Royal Astronomical Society 449(1), 835 (2015) https://doi.org/10.1093/mnras/stv154 Alam et al. [2017] Alam, U., Bag, S., Sahni, V.: Constraining the cosmology of the phantom brane using distance measures. Physical Review D 95(2), 023524 (2017) https://doi.org/10.1103/PhysRevD.95.023524 Zhao et al. [2019] Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Alam, U., Bag, S., Sahni, V.: Constraining the cosmology of the phantom brane using distance measures. Physical Review D 95(2), 023524 (2017) https://doi.org/10.1103/PhysRevD.95.023524 Zhao et al. [2019] Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  5. Ross, A.J., Samushia, L., Howlett, C., et al.: The clustering of the SDSS DR7 main Galaxy sample - I. A 4 per cent distance measure at z = 0.15. Monthly Notices of the Royal Astronomical Society 449(1), 835 (2015) https://doi.org/10.1093/mnras/stv154 Alam et al. [2017] Alam, U., Bag, S., Sahni, V.: Constraining the cosmology of the phantom brane using distance measures. Physical Review D 95(2), 023524 (2017) https://doi.org/10.1103/PhysRevD.95.023524 Zhao et al. [2019] Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Alam, U., Bag, S., Sahni, V.: Constraining the cosmology of the phantom brane using distance measures. Physical Review D 95(2), 023524 (2017) https://doi.org/10.1103/PhysRevD.95.023524 Zhao et al. [2019] Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  6. Alam, U., Bag, S., Sahni, V.: Constraining the cosmology of the phantom brane using distance measures. Physical Review D 95(2), 023524 (2017) https://doi.org/10.1103/PhysRevD.95.023524 Zhao et al. [2019] Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  7. Zhao, G.-B., Wang, Y., Saito, S., et al.: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights. Monthly Notices of the Royal Astronomical Society 482(3), 3497 (2019) https://doi.org/10.1093/mnras/sty2845 Ichiki and Nagata [2009] Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  8. Ichiki, K., Nagata, R.: Brute force reconstruction of the primordial fluctuation spectrum from five-year Wilkinson Microwave Anisotropy Probe observations. Physical Review D 80(8), 083002 (2009) https://doi.org/10.1103/PhysRevD.80.083002 Komatsu et al. [2011] Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  9. Komatsu, E., Smith, K.M., Dunkley, J., et al.: Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. The Astrophysical Journal Supplement Series 192(2), 18 (2011) https://doi.org/10.1088/0067-0049/192/2/18 Planck Collaboration et al. [2016] Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  10. Planck Collaboration, Ade, P.A.R., Aghanim, N., et al.: Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics 594, A13 (2016) https://doi.org/10.1051/0004-6361/201525830 Planck Collaboration et al. [2020] Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  11. Planck Collaboration, Aghanim, N., Akrami, Y., et al.: Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics 641, A6 (2020) https://doi.org/10.1051/0004-6361/201833910 Freedman and Madore [2010] Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  12. Freedman, W.L., Madore, B.F.: The Hubble Constant. Annual Review of Astronomy and Astrophysics 48, 673 (2010) https://doi.org/10.1146/annurev-astro-082708-101829 Riess et al. [2016] Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  13. Riess, A.G., Macri, L.M., Hoffmann, S.L., et al.: A 2.4% Determination of the Local Value of the Hubble Constant. The Astrophysical Journal 826(1), 56 (2016) https://doi.org/10.3847/0004-637X/826/1/56 Riess et al. [2018] Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  14. Riess, A.G., Rodney, S.A., Scolnic, D.M., et al.: Type Ia Supernova Distances at Redshift >>>1.5 from the Hubble Space Telescope Multi-cycle Treasury Programs: The Early Expansion Rate. The Astrophysical Journal 853(2), 126 (2018) https://doi.org/10.3847/1538-4357/aaa5a9 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  15. Riess, A.G., Casertano, S., Yuan, W., et al.: Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Riess et al. [2022a] Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  16. Riess, A.G., Yuan, W., Macri, L.M., et al.: A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Mpc−11{}^{-1}start_FLOATSUPERSCRIPT - 1 end_FLOATSUPERSCRIPT Uncertainty from the Hubble Space Telescope and the SH0ES Team. The Astrophysical Journal Letters 934(1), L7 (2022) https://doi.org/10.3847/2041-8213/ac5c5b Riess et al. [2022b] Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  17. Riess, A.G., Breuval, L., et al.: Cluster Cepheids with High Precision Gaia Parallaxes, Low Zero-point Uncertainties, and Hubble Space Telescope Photometry. The Astrophysical Journal 938(1), 36 (2022) https://doi.org/10.3847/1538-4357/ac8f24 Li and Shafieloo [2019] Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  18. Li, X., Shafieloo, A.: A Simple Phenomenological Emergent Dark Energy Model can Resolve the Hubble Tension. The Astrophysical Journal Letters 883(1), L3 (2019) https://doi.org/10.3847/2041-8213/ab3e09 Pan et al. [2020] Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  19. Pan, S., Yang, W., Di Valentino, E., et al.: Reconciling H00{}_{0}start_FLOATSUBSCRIPT 0 end_FLOATSUBSCRIPT tension in a six parameter space? Journal of Cosmology and Astroparticle Physics 2020(6), 062 (2020) https://doi.org/10.1088/1475-7516/2020/06/062 Koo et al. [2020] Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  20. Koo, H., Shafieloo, A., Keeley, R.E., et al.: Model-independent Constraints on Type Ia Supernova Light-curve Hyperparameters and Reconstructions of the Expansion History of the Universe. The Astrophysical Journal 899(1), 9 (2020) https://doi.org/10.3847/1538-4357/ab9c9a Yang et al. [2023] Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  21. Yang, W., Giarè, W., Pan, S., et al.: Revealing the effects of curvature on the cosmological models. Physical Review D 107(6), 063509 (2023) https://doi.org/10.1103/PhysRevD.107.063509 Liu et al. [2022] Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  22. Liu, T., Cao, S., Li, X., et al.: Revising the Hubble constant, spatial curvature and dark energy dynamics with the latest observations of quasars. Astronomy & Astrophysics 668, A51 (2022) https://doi.org/10.1051/0004-6361/202243375 Li and Shafieloo [2020] Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  23. Li, X., Shafieloo, A.: Evidence for Emergent Dark Energy. The Astrophysical Journal 902(1), 58 (2020) https://doi.org/10.3847/1538-4357/abb3d0 Motta et al. [2021] Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  24. Motta, V., García-Aspeitia, M.A., Hernández-Almada, A., et al.: Taxonomy of Dark Energy Models. Universe 7(6), 163 (2021) https://doi.org/10.3390/universe7060163 Dainotti et al. [2021] Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  25. Dainotti, M.G., De Simone, B., Schiavone, T., et al.: On the Hubble Constant Tension in the SNe Ia Pantheon Sample. The Astrophysical Journal 912(2), 150 (2021) https://doi.org/10.3847/1538-4357/abeb73 Tanvir et al. [2009] Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  26. Tanvir, N.R., Fox, D.B., Levan, A.J., et al.: A γ𝛾\gammaitalic_γ-ray burst at a redshift of z≈8.2𝑧8.2z\approx 8.2italic_z ≈ 8.2. Nature 461(7268), 1254 (2009) https://doi.org/10.1038/nature08459 Cucchiara et al. [2011] Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  27. Cucchiara, A., Levan, A.J., Fox, D.B., et al.: A Photometric Redshift of z∼9.4similar-to𝑧9.4z\sim 9.4italic_z ∼ 9.4 for GRB 090429B. The Astrophysical Journal 736(1), 7 (2011) https://doi.org/10.1088/0004-637X/736/1/7 Dai et al. [2004] Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  28. Dai, Z.G., Liang, E.W., Xu, D.: Constraining ΩΩ\Omegaroman_ΩM𝑀{}_{M}start_FLOATSUBSCRIPT italic_M end_FLOATSUBSCRIPT and Dark Energy with Gamma-Ray Bursts. The Astrophysical Journal 612(2), L101 (2004) https://doi.org/10.1086/424694 Ghirlanda et al. [2006] Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  29. Ghirlanda, G., Ghisellini, G., Firmani, C.: Gamma-ray bursts as standard candles to constrain the cosmological parameters. New Journal of Physics 8(7), 123 (2006) https://doi.org/10.1088/1367-2630/8/7/123 Liang et al. [2008] Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  30. Liang, N., Xiao, W.K., Liu, Y., et al.: A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram. The Astrophysical Journal 685(1), 354 (2008) https://doi.org/10.1086/590903 Liang et al. [2010] Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  31. Liang, N., Wu, P., Zhang, S.N.: Constraints on cosmological models and reconstructing the acceleration history of the universe with gamma-ray burst distance indicators. Physical Review D 81(8), 083518 (2010) https://doi.org/10.1103/PhysRevD.81.083518 Liang et al. [2011] Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  32. Liang, N., Xu, L., Zhu, Z.-H.: Constraints on the generalized Chaplygin gas model including gamma-ray bursts via a Markov Chain Monte Carlo approach. Astronomy & Astrophysics 527, A11 (2011) https://doi.org/10.1051/0004-6361/201015919 Wei [2010] Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  33. Wei, H.: Observational constraints on cosmological models with the updated long gamma-ray bursts. Journal of Cosmology and Astroparticle Physics 2010(8), 020 (2010) https://doi.org/10.1088/1475-7516/2010/08/020 Wang et al. [2016] Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  34. Wang, J.S., Wang, F.Y., Cheng, K.S., Dai, Z.G.: Measuring dark energy with the Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT - Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT correlation of gamma-ray bursts using model-independent methods. Astronomy & Astrophysics 585, A68 (2016) https://doi.org/10.1051/0004-6361/201526485 Liu et al. [2022] Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  35. Liu, Y., Liang, N., Xie, X., Yuan, Z., Yu, H., Wu, P.: Gamma-Ray Burst Constraints on Cosmological Models from the Improved Amati Correlation. The Astrophysical Journal 935(1), 7 (2022) https://doi.org/10.3847/1538-4357/ac7de5 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  36. Jimenez, R., Loeb, A.: Constraining cosmological parameters based on relative galaxy ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2022] Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  37. Moresco, M., Amati, L., Amendola, L., et al.: Unveiling the Universe with emerging cosmological probes. Living Reviews in Relativity 25(1), 6 (2022) https://doi.org/10.1007/s41114-022-00040-z Amati et al. [2019] Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  38. Amati, L., D’Agostino, R., Luongo, O., Muccino, M., Tantalo, M.: Addressing the circularity problem in the Ep𝑝{}_{p}start_FLOATSUBSCRIPT italic_p end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation of gamma-ray bursts. Monthly Notices of the Royal Astronomical Society: Letters 486(1), L46 (2019) https://doi.org/10.1093/mnrasl/slz056 Demianski et al. [2017] Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  39. Demianski, M., Piedipalumbo, E., Sawant, D., Amati, L.: Cosmology with gamma-ray bursts. I. The Hubble diagram through the calibrated Ep,I𝑝𝐼{}_{p,I}start_FLOATSUBSCRIPT italic_p , italic_I end_FLOATSUBSCRIPT-Ei⁢s⁢o𝑖𝑠𝑜{}_{iso}start_FLOATSUBSCRIPT italic_i italic_s italic_o end_FLOATSUBSCRIPT correlation. Astronomy & Astrophysics 598, A112 (2017) https://doi.org/10.1051/0004-6361/201628909 Li et al. [2023] Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  40. Li, Z., Zhang, B., Liang, N.: Testing dark energy models with gamma-ray bursts calibrated from the observational H(z) data through a Gaussian process. Monthly Notices of the Royal Astronomical Society 521(3), 4406 (2023) https://doi.org/10.1093/mnras/stad838 Xie et al. [2023] Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  41. Xie, H., Nong, X., Zhang, B., et al.: Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way. arXiv e-prints, 2307–16467 (2023) https://doi.org/10.48550/arXiv.2307.16467 Jia et al. [2023] Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  42. Jia, X.D., Hu, J.P., Wang, F.Y.: Evidence of a decreasing trend for the Hubble constant. Astronomy & Astrophysics 674, A45 (2023) https://doi.org/10.1051/0004-6361/202346356 Hernández-Almada et al. [2020] Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  43. Hernández-Almada, A., Leon, G., Magaña, J., García-Aspeitia, M.A., Motta, V.: Generalized emergent dark energy: observational Hubble data constraints and stability analysis. Monthly Notices of the Royal Astronomical Society 497(2), 1590 (2020) https://doi.org/10.1093/mnras/staa2052 Liang et al. [2022] Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  44. Liang, N., Li, Z., Xie, X., et al.: Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae. The Astrophysical Journal 941(1), 84 (2022) https://doi.org/10.3847/1538-4357/aca08a Chevallier and Polarski [2001] Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  45. Chevallier, M., Polarski, D.: Accelerating Universes with Scaling Dark Matter. International Journal of Modern Physics D 10(2), 213 (2001) https://doi.org/10.1142/S0218271801000822 Linder [2003] Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  46. Linder, E.V.: Cosmic shear with next generation redshift surveys as a cosmological probe. Physical Review D 68(8), 083503 (2003) https://doi.org/10.1103/PhysRevD.68.083503 Linder [2005] Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  47. Linder, E.V.: Cosmic growth history and expansion history. Physical Review D 72(4), 043529 (2005) https://doi.org/10.1103/PhysRevD.72.043529 Barger et al. [2006] Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  48. Barger, V., Guarnaccia, E., Marfatia, D.: Classification of dark energy models in the (w0,wasubscript𝑤0subscript𝑤𝑎w_{0},w_{a}italic_w start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_w start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT) plane. Physics Letters B 635(2-3), 61 (2006) https://doi.org/10.1016/j.physletb.2006.02.018 Khadka et al. [2021] Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  49. Khadka, N., Luongo, O., Muccino, M., et al.: Do gamma-ray burst measurements provide a useful test of cosmological models? Journal of Cosmology and Astroparticle Physics 2021(9), 042 (2021) https://doi.org/10.1088/1475-7516/2021/09/042 Jimenez and Loeb [2002] Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  50. Jimenez, R., Loeb, A.: Constraining Cosmological Parameters Based on Relative Galaxy Ages. The Astrophysical Journal 573(1), 37 (2002) https://doi.org/10.1086/340549 Moresco et al. [2020] Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  51. Moresco, M., Jimenez, R., Verde, L., et al.: Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix. The Astrophysical Journal 898(1), 82 (2020) https://doi.org/10.3847/1538-4357/ab9eb0 Moresco et al. [2012] Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  52. Moresco, M., Cimatti, A., Jimenez, R., et al.: Improved constraints on the expansion rate of the Universe up to z ∼similar-to\sim∼1.1 from the spectroscopic evolution of cosmic chronometers. Journal of Cosmology and Astroparticle Physics 2012(8), 006 (2012) https://doi.org/10.1088/1475-7516/2012/08/006 Moresco [2015] Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  53. Moresco, M.: Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z∼2similar-to𝑧2z\sim 2italic_z ∼ 2. Monthly Notices of the Royal Astronomical Society 450, 16–20 (2015) https://doi.org/10.1093/mnrasl/slv037 Moresco et al. [2016] Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  54. Moresco, M., Pozzetti, L., Cimatti, A., et al.: A 6% measurement of the Hubble parameter at z∼similar-to\sim∼0.45: direct evidence of the epoch of cosmic re-acceleration. Journal of Cosmology and Astroparticle Physics 2016(5), 014 (2016) https://doi.org/10.1088/1475-7516/2016/05/014 Foreman-Mackey et al. [2013] Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  55. Foreman-Mackey, D., Hogg, D.W., Lang, D., et al.: emcee: The MCMC Hammer. Publications of the Astronomical Society of the Pacific 125(925), 306 (2013) https://doi.org/10.1086/670067 Newville et al. [2021] Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  56. Newville, M., Otten, R., Nelson, A., et al.: Lmfit/lmfit-py:. https://doi.org/10.5281/zenodo.4516644 Lewis [2019] Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  57. Lewis, A.: GetDist: a Python package for analysing Monte Carlo samples. arXiv e-prints, 1910 (2019) https://doi.org/10.48550/arXiv.1910.13970 Riess et al. [2019] Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  58. Riess, A.G., Casertano, S., Yuan, W., et al.: Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛΛ\Lambdaroman_ΛCDM. The Astrophysical Journal 876(1), 85 (2019) https://doi.org/10.3847/1538-4357/ab1422 Akaike [1974] Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  59. Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716 (1974) https://doi.org/10.1109/TAC.1974.1100705 Schwarz [1978] Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  60. Schwarz, G.: Estimating the dimension of a model. The annals of statistics, 6(2), 416 (1978) https://doi.org/10.1214/aos/1176344136 Kunz et al. [2006b] Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  61. Kunz, M., Trotta, R., Parkinson, D.R.: Measuring the effective complexity of cosmological models. Physical Review D 74(2), 023503 (2006) https://doi.org/10.1103/PhysRevD.74.023503 Spiegelhalter et al. [2002] Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353 Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
  62. Spiegelhalter, D., Best, N., Carlin, B.: Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64, 583 (2002) https://doi.org/10.1111/1467-9868.00353
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